Truth, Hierarchy, and Incoherence

According to this chapter, approaches to truth and to the liar paradox appear to face a dilemma, as they must, it seems, appeal to some sort of hierarchy or contend that a putatively coherent concept is actually incoherent, either of which results in expressive limitations. The chapter proposes a new approach to the liar paradox that avoids such expressive limitations. This approach countenances classical semantic values while advocating a revision to how we think about compositional rules. The idea is that there are exceptions to the compositional rules associated with a language. To this end, the chapter adverts to theories that respect the “Chrysippus intuition,” which captures the idea that different tokens of the same type can have divergent semantic statuses. Such theories yield models of languages whose semantic values are classical but where the compositional rules associated with these languages have exceptions.